Chapter 16. Portfolio Performance Measurement and Evaluation

HPR = [Income + (End value − Begin value)] ÷ Begin value

Example →

₹1 lakh grows to ₹1.2 lakh plus ₹5,000 dividend → (5,000 + 20,000) ÷ 1,00,000 = 25%.

Trap →

Leaving out the income shows 20% instead of 25%. Annualise HPRs for periods longer than a year.

TWRR = [Π (1 + HPRᵢ)]^(1/n) − 1 (chain-linked sub-period returns)

Example →

Yearly returns −5%, −15.2%, 8.1%, 30.75%, 17.65% → product 1.3396 → 6.02% a year.

Trap →

Taking the arithmetic mean (7.26%) overstates it. TWRR removes the effect of client cash flows; SEBI mandates TWRR for PMS performance disclosure.

MWRR = IRR of all client cash flows (contributions, withdrawals and ending value)

Excel: IRR(values) · XIRR(values, dates)

Example →

Answers 'how much did this client actually earn?', so it's sensitive to the timing and size of contributions.

Trap →

Don't confuse it with TWRR. MWRR suits client-level reports; manager comparison and PMS disclosure use TWRR.

AMR = ΣR ÷ n · GMR = [Π (1 + Rᵢ)]^(1/n) − 1 · GMR ≤ AMR

Example →

Returns −50% then +100% → AMR 25%, but GMR 0% (the money is flat).

Trap →

AMR presented as the actual long-run return is wrong; GMR (CAGR) reflects what the investor earned.

CAGR = (End ÷ Begin)^(1/t) − 1

Example →

₹1,00,000 → ₹1,33,960 in 5 years → 1.3396^0.2 − 1 = 6.02%.

Trap →

Not appropriate for periods under one year.

Post-tax = Pre-tax × (1 − t) · Pre-tax = Post-tax ÷ (1 − t)

Example →

Pre-tax 5% at a 15% tax rate → 4.25% post-tax. Needing 8.4% post-tax in the 30% slab → 12% pre-tax.

Trap →

Multiply by (1 − t); don't subtract the tax rate from the return.

Adjusted return = (w_equity × R_equity + w_cash × R_cash) ÷ Total capital

Example →

₹100 lakh: ₹75 lakh in equity at 10%, ₹25 lakh in liquid funds at 4% → (7.5 + 1) ÷ 100 = 8.5%, not 10%.

Trap →

Reporting the return only on the invested ₹75 lakh inflates it. Measure on total capital.

βp = Σ wᵢ × βᵢ (weighted average)

Example →

A: β 1.2 at 60%, B: β 1.1 at 40% → 0.72 + 0.44 = 1.16.

Trap →

Beta is linear in weights, but portfolio SD isn't; SD needs the correlations.

Required return = Rf + β × (Rm − Rf)

Example →

Rf 5%, β 1.5, Rm 15% → 5 + 1.5 × 10 = 20%.

Trap →

If the equity risk premium (Rm − Rf) is given directly, don't subtract Rf from it again.

α = Rp − [Rf + β × (Rm − Rf)]

Example →

Rp 25%, Rf 5%, β 1.5, Rm 15% → 25 − 20 = +5%.

Trap →

Alpha isn't 'return over the benchmark' (25 − 15 = 10%); it's return over the CAPM-required return.

Sharpe = (Rp − Rf) ÷ σp (total risk)

Example →

Rp 10.50%, Rf 5.50%, σ 6.50% → 5 ÷ 6.50 = 0.769.

Trap →

Using β in the denominator gives Treynor. Sharpe suits a standalone (only) portfolio.

Treynor = (Rp − Rf) ÷ βp (systematic risk only)

Example →

Rp 10.50%, Rf 5.50%, β 1 → 5.0 (percentage points of excess return per unit of beta).

Trap →

Treynor suits a holding within an already well-diversified portfolio, not an under-diversified one.

Sortino = (Rp − Rf) ÷ Downside (semi) standard deviation

Example →

Only downside volatility is penalised, which suits investors who define risk as the chance of losing money.

Trap →

Using total SD in the denominator gives Sharpe, not Sortino.

IR = (Rp − Rb) ÷ Tracking error · Tracking error = SD(Rp − Rb)

Example →

Active return 2%, tracking error 4% → IR 0.50. It shows whether alpha comes from skill or luck.

Trap →

The denominator is the SD of the return difference (tracking error), not the portfolio's total SD. Tracking error isn't the same as tracking difference.

w = σm ÷ σp · M² return = w × Rp + (1 − w) × Rf

Example →

Rp 35%, σp 42%; Rm 28%, σm 30%; Rf 6% → w = 0.714 → M² = 26.7%, below the market's 28%: underperformed on a risk-adjusted basis.

Trap →

Comparing raw returns (35% > 28%) is wrong; first scale the portfolio to market risk with T-bills.

Net selectivity = (Rp − Rf) − [(Rm − Rf) ÷ σm × σp]

Example →

Rp 18%, Rf 6%, Rm 14%, σm 15%, σp 20% → 12 − 10.67 = 1.33%. Positive means genuine selection skill.

Trap →

Not Jensen's alpha: Fama scales by total risk (σ), Jensen uses systematic risk (β).

₹ return ≈ Local-currency return + % change in the exchange rate (₹ per foreign unit)

Example →

₹50 lakh at ₹70/$ = $71,428.57; earns 15% → $82,142.86; rupee appreciates to ₹65/$ → ₹53.39 lakh, a ₹ return of 6.79%.

Trap →

Rupee appreciation reduces the ₹ return on foreign assets; depreciation adds to it.